FIGS. 1A and 1B illustrate a prior-art Hybrid Fiber-Coax (HFC) cable system 100 that is compatible with the cable industry standard Data over Cable System Interface Specification (DOCSIS) for providing Internet access to cable customers via so called Cable Modems (CMs). FIG. 1A is a top-level view of the cable system. FIG. 1B provides additional detail of the Customer Premises Equipment (CPE) of FIG. 1A. In FIG. 1B, CM 4000 provides a computer industry standard Ethernet interface to PC 5000 and bridges the Ethernet interface with the coax distribution of the cable system. CM 4000 internally implements both an RF Modulator and an RF Demodulator for communications over the coax in accordance with the DOCSIS standard.
An RF Modulator 3000 and RF Demodulator 1000, complementary to those of the cable modem, are implemented in a DOCSIS compatible Cable Modem Termination System (CMTS) 500, which as the name implies, provides termination for the Cable Modem of the CPE. Multiple instances of Modulator 3000 and Demodulator 1000 are provisioned to support all customers with CM service. Control, MAC, Framing 2000 bridges all of the provisioned DOCSIS RF interfaces with one or more packet-based networks. These packet networks may include local area networks, intranets, and the Internet. While FIG. 1A shows the CMTS 500 implemented in a Head End or Primary Hub, theoretically it is possible to implement the CMTS anywhere upstream from the CM. Each demodulator 1000 provides outputs to the Control, MAC, Framing 2000 that include Detected Symbols 1200 and a Frequency Offset Estimate 1300.
While the transmitter of the CM upstream modulator and the complementary receiver in the CMTS demodulator are theoretically provisioned for identical frequencies, frequency offsets may occur for a variety of reasons. These reasons include errors in the local oscillators of the CM modulator (used to transmit the signal burst at the provisioned frequency) or CMTS front-end (used to down-convert the received signal burst to baseband) as well as the use of up- and downconversion processes applied to the upstream channels over the path from CM to CMTS. These conversion processes are used to combine and split multiple channels over common communication paths for economic transport. Depending on severity and other system issues, frequency offsets could degrade Bit Error Rates (BERs), increase latencies, or completely prevent signal capture. However, these problems may be avoided by using closed loop methods to minimize or eliminate the offsets.
In CMTS applications, system operation may be conceptually divided into normal data traffic conditions (traffic mode) and so-called ranging periods (ranging mode). Ranging is a closed loop process by which the CMTS manages the timing, power level, offset frequency, and equalization for the transmitter of each CM. Ranging is performed whenever a CM is initialized and registered by the network and also periodically (at regular time intervals) to update its calibration. The ranging calibration process is performed for every CM on the channel and enables the system to smoothly operate at high effective throughput during traffic mode.
As applicable to the cable system of FIG. 1A, during ranging, a Frequency Offset Estimate 1300 is made in Demodulator 1000 of the CMTS and provided to the Control, MAC, and Framing 2000. The control functions of this block then send one or more commands downstream to the corresponding CM, remotely adjusting its transmitter frequency until the frequency offset observed at Demodulator 1000 is reduced to within predefined acceptable limits. Once set during ranging, the offset frequency adjust continues to be used by the CM during subsequent traffic mode operation. The ranging determined offset frequency adjust thus effectively eliminates any frequency offset observed by the CMTS, regardless of the source or sources of the offset.
Ranging represents the most problematic operating condition for determining the frequency offset estimate, as the frequency offset is generally large during ranging and other CM characteristics are not yet calibrated for optimal performance. Accordingly, symbol errors may be frequent. During traffic mode, the CM is operating with a much smaller effective frequency offset due to the compensating offset frequency adjust assigned by the CMTS during ranging and overall CM operation is optimally calibrated. Symbol errors are significantly reduced.
Demodulator Operation
FIG. 2A provides a general conceptual block diagram of the digital burst Demodulator 1000 in the CMTS 500. Front-End 600 isolates one modulated carrier from the carrier multiplex in the Received Spectrum 1100, baseband converts the signal, and passes the resulting signal 1105 to the Burst and Timing Synchronization circuit 1500. (In other contexts the Front-End 600 might be considered as a function prior to, and not part of, the demodulator.) The Recovered Signal Samples 1106, at the output of circuit 1500, are discrete signal samples at the symbol rate.
Equalizer 1600 compensates for signal distortion not compensated by a pre-equalizer in the cable modem (CM) and also suppresses ingress noise. At the output of this stage, the Equalized Signal Samples rk (1107) are given by:rk=akejφk+wk,where ak is the transmitted symbol and wk is the additive noise. These samples are not yet synchronized in terms of carrier phase.
Carrier Phase Synchronized Samples 1108 are produced by the Rotator 1700 in conjunctions with Phase Estimator 1900. The carrier phase φk is given by:φk=2kπΔfTs+φ0.where Δf is the frequency offset and Ts is the symbol period.
Let {circumflex over (φ)}k be the estimated carrier phase used for symbol k. The equalized signal rk is multiplied by exp(−j{circumflex over (φ)}k) within Rotator 1700 so as to decide symbol ak by Detector 1800. The decision on symbol ak is denoted dk, which is output as Detected Symbols 1200.
The quantity pk=rkd*k is subsequently computed. For CMTS and other applications having a high value of the frequency drift, quasi-differential demodulation is preferred, and the carrier phase recovery algorithm only uses the last value of pk to determine the carrier phase. In such cases, the estimated carrier phase can thus be written as:{circumflex over (φ)}k=arg(rk−1d*k−1)Prior Art Frequency Estimators
Frequency Offset Estimator 8000 provides Frequency Offset Estimate 1300, an estimate of the observed frequency offset of the received signal. Prior art frequency estimation techniques for general burst demodulator applications have used phase slope computations and related time averaging, or have been based on the autocorrelation function of the signal. FIG. 2B illustrates a particular prior art Frequency Offset Estimator (8000-PA-AC) based on autocorrelation of the signal. FIG. 2C illustrates a particular prior art Frequency Offset Estimator (8000-PA-PS) based on phase slope computations. FIG. 2D provides additional detail of the Phase Slope Computation 8100, of FIG. 2C.
The prior art frequency estimation techniques provide satisfactory precision for more general burst demodulator applications that use long bursts of known symbols (such as found in long message preambles) or admit to time averaging over multiple consecutive bursts. Unfortunately, both isolated short bursts and symbol errors are characteristics of CMTS applications, particularly during ranging. CMTS applications employ isolated short ranging bursts of approximately 200 symbols, consisting of a very short preamble (typically 20-30 known symbols) and a short data block consisting of symbols extracted by the local detector. Due to noise and other factors, generally including the existence of frequency offsets, the output of the detector will not be free of symbol errors.
In view of the above, it is useful to make a detailed examination of the performance of the prior art frequency estimator based on the autocorrelation function of the signal. As shown in FIG. 2B, the prior art autocorrelation estimator bases the frequency estimation on the computation of δk=pkP*k−L. By proper normalization of the time average of δk, the frequency can be estimated as:
            Δ      ⁢                          ⁢      f        ^    =            arg      ⁡              (                              ∑                          k              =                              L                +                1                                      N                    ⁢                      δ            k                          )                    2      ⁢                          ⁢      π      ⁢                          ⁢              T        s            ⁢      L      
where N designates the number of symbols in the burst at hand, and L is a delay parameter defined in the Correlator 8620 in FIG. 2B.
Suppose that a symbol error occurs at the k0 decision instant. With the assumed QPSK signal format, this leads to an instantaneous phase error of ±π/2. Furthermore, as quasi-differential demodulation is used, this ±π/2 phase-error appears in all subsequent symbol decisions, and also in all Pk values computed after k0.
Thus, the phase of pk for the theoretical frequency estimator has a constant slope except for one discontinuity of ±π/2 when the error occurs. Consequently, the phase of δk (recall that δk=pkP*k−L) is centered around the desired value, except for L values with an error of ±π/2. The average phase of δk over the burst size is then shifted by ±L(π/2)/(N−L). Since the normalized frequency estimate ΔfTs is obtained by dividing this average phase by 2πL, it clearly contains an error of ±0.25/(N−L).
Consider a particular quantitative example using the foregoing analysis Suppose that we want to have an estimation precision of 10−4 for a burst length of 200. Should a single decision error occur during this burst, this error would result in a normalized frequency estimation error of approximately 0.25/200, or approximately 10−3. This is an order of magnitude greater than the desired accuracy of 10−4. Those skilled in the art will see that a similar analysis, with similar results, can be made for a phase slope based estimator.
The prior art frequency estimation approaches are clearly not well suited to CMTS applications, as it has been seen that even a single symbol error results in substantial errors. Improved frequency estimation methods and devices are needed that provide precise frequency estimates for short bursts in the presence of symbol errors. New frequency estimation approaches are needed that can be performed on one single burst, without the need for averaging the results of several consecutive bursts. In particular, improved frequency estimation techniques are needed that offer superior performance for CMTS applications.